Related papers: Negative refraction and tiling billiards
When an oscillating line source is placed in front of a special mirror consisting of an array of flat uniformly spaced ferrite rods, half of the image disappeared at some frequency. We believe that this comes from the coupling to photonic…
Several articles deal with tilings with squares and dominoes on 2-dimensional boards, but only a few on boards in 3-dimensional space. We examine a tiling problem with colored cubes and bricks of $(2\times2\times n)$-board in three…
We study the tiling of a two-dimensional region of the plane by $K$-cell one-dimensional tiles, or $K$-mers. Unlike previous studies, which typically allowed for one single value of $K$ or sometimes a small assortment of fixed values, here…
The question of invisibility for bodies with mirror surface is studied in the framework of geometrical optics. We construct bodies that are invisible/have zero resistance in two mutually orthogonal directions, and prove that there do not…
We propose a generic mechanism for the formation of narrow rings in rotating systems. For this purpose we use a system of discs rotating about a common center lying well outside the discs. A discussion of this system shows that narrow rings…
A body moves in a medium composed of noninteracting point particles; interaction of particles with the body is absolutely elastic. It is required to find the body's shape minimizing or maximizing resistance of the medium to its motion. This…
This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to establish conjugacy properties of tiling spaces. Tiles may be…
Metamaterials are artificial composite materials that, by virtue of their microstructure, exhibit properties not exhibited by their component materials. Much excitement has been generated by negatively refracting metamaterials, typically…
The extraordinary properties of resonant four-wave mixing of backward waves in doped negative-index materials are investigated. The feasibility of independent engineering of negative refractive index and nonlinear optical response as well…
The paper considers an opportunity for the creation of an artificial two-component metamaterial with a negative refractive index within the radio and optical frequency band, which possesses a spatial dispersion. It is shown that there…
We show that negative refraction with minimal absorption can be obtained by means of quantum interference effects similar to electromagnetically induced transparency. Coupling a magnetic dipole transition coherently with an electric dipole…
The existence of normal deterministic diffusion in dynamical systems with a two-dimensional phase space tiled by regular triangles (or their unions into regular hexagons) is proven.
We define a new class of plane billiards - the `pensive billiard' - in which the billiard ball travels along the boundary for some distance depending on the incidence angle before reflecting, while preserving the billiard rule of equality…
Pinwheel patterns and their higher dimensional generalisations display continuous circular or spherical symmetries in spite of being perfectly ordered. The same symmetries show up in the corresponding diffraction images. Interestingly, they…
The top of the attractor $A$ of a hyperbolic iterated function system $\left\{ f_{i}:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}|i=1,2,\dots,M\right\} $ is defined and used to extend self-similar tilings to overlapping systems. The theory…
We investigate the transmission and reflection survival probabilities for the chaotic stadium billiard with two holes placed asymmetrically. Classically, these distributions are shown to have algebraic or exponential decays depending on the…
A method is described for constructing, with computer assistance, planar substitution tilings that have n-fold rotational symmetry. This method uses as prototiles the set of rhombs with angles that are integer multiples of pi/n, and…
The tiling problem has been a famous problem that has appeared in many Mathematics problems. Many of its solutions are rooted in high-level Mathematics. Thus we hope to tackle this problem using more elementary Mathematics concepts. In this…
We perform classical three-dimensional Monte Carlo simulations of ultracold neutrons scattering through an absorbing-reflecting mirror system in the Earth's gravitational field. We show that the underlying mixed phase space of regular…
We study a class of dynamical systems which generalizes and unifies some models arising in the analysis of switched flow systems in manufacturing. General properties of these dynamical systems, called pseudo billiards, as well as some their…